A general method for obtaining degenerate solutions to the Dirac and Weyl equations and a discussion on the experimental detection of degenerate states

TL;DR

This paper introduces a universal method to generate degenerate solutions to the Dirac and Weyl equations, revealing localized solutions for massive particles and proposing experimental detection techniques for these states.

Contribution

The authors develop a general approach to construct degenerate solutions for Dirac and Weyl equations using arbitrary functions, expanding understanding of their properties and potential observability.

Findings

Constructed explicit solutions for infinite electromagnetic potentials

Demonstrated localization of solutions for massive Dirac particles

Proposed experimental detection methods for degenerate states

Abstract

In this work we describe a general method for obtaining degenerate solutions to the Dirac equation, corresponding to an infinite number of electromagnetic 4-potentials and fields, which are explicitly calculated. In more detail, using four arbitrary real functions, one can automatically construct a spinor which is solution to the Dirac equation for an infinite number of electromagnetic 4-potentials, defined by those functions. An interesting characteristic of these solutions is that, in the case of Dirac particles with non-zero mass, the degenerate spinors should be localized, both in space and time. Our method is also extended to the cases of massless Dirac and Weyl particles, where the localization of the spinors is no longer required. Finally, we propose two experimental methods for detecting the presence of degenerate states.